Russia on Wednesday accused Turkey of a "planned provocation" over the downing of a warplane on the Syrian border but pledged not to go to war as NATO-member Ankara sought to play down tensions.

As the diplomatic fallout from Tuesday's incident raged on, Moscow said Russian and Syrian special forces had rescued one of the pilots who ejected from the burning Russian plane but confirmed the second airman was dead.

The jet downing has threatened ties between two major rival players in the Syrian war and raised fears it could escalate into a wider geopolitical conflict.

Russian Foreign Minister Sergei Lavrov ratcheted up the pressure after talking to Turkish counterpart Mevlut Cavusoglu by phone in the first contact between the two sides since the plane went down.

"We have serious doubts about this being an unpremeditated act, it really looks like a planned provocation," Lavrov said at a press conference in Moscow.

"We do not plan to go to war with Turkey, our attitude toward the Turkish people has not changed," Lavrov added, but warned that Moscow would "seriously reevaluate" relations with Ankara.

President Vladimir Putin on Tuesday branded the incident a "stab in the back committed by accomplices of terrorists", recommending that Russians do not visit Turkey, a key tourist destination.

- 'Friend and neighbour' -

Turkey, however, has sought to turn down the heat, with President Recep Tayyip Erdogan insisting Ankara was simply defending its border.

"We have no intention to escalate this incident. We are just defending our security and the rights of our brothers," Erdogan said in a speech in Istanbul.

Prime Minister Ahmet Davutoglu called Russia "our friend and our neighbour" and said Ankara did not want to strain ties with Moscow.

Turkey says the Su-24 warplane violated its airspace 10 times within a five-minute period, but Russia insisted it never strayed from Syrian territory.

The shooting also risks derailing efforts to bring peace to Syria that were gaining tentative momentum following the November 13 Paris attacks claimed by Islamic State militants who control swathes of northern Syria.

US President Barack Obama said Washington's NATO ally had a right to defend its airspace but said his priority was to make sure the standoff did not escalate.

Following an extraordinary meeting of the alliance Tuesday, NATO chief Jens Stoltenberg said "diplomacy and de-escalation are important to resolve this situation".

- 'Necessary measure' -

Turkey's ambassador to the United Nations Halit Cevik said in a letter to the Security Council that two planes were involved, one of which was shot down while the other left Turkish airspace.

He said both had flown 1.36 miles (2.19 kilometres) into Turkish airspace for 17 seconds from 0724 GMT Tuesday.

Ankara and Moscow are already on starkly opposing sides in the four-year Syrian civil war, with Turkey wanting to see the ouster of President Bashar al-Assad while Russia is one of his last remaining allies.